1 Automata: The Methods and the Madness
1.1 Why Study Automata Theory?
1.1.1 Introduction to Finite Automata
1.1.2 Structural Representations
1.1.3 Automata and Complexity
1.2 Introduction to Formal Proof
1.2.1 Deductive Proofs
1.2.2 Reduction to Definitions
1.2.3 Other Theorem Forms
1.2.4 Theorems That Appear Not to Be If-Then Statements
1.3 Additional Forms of Proof
1.3.1 Proving Equivalences About Sets
1.3.2 The Contrapositive
1.3.3 Proof by Contradiction
1.3.4 Counterexamples
1.4 Inductive Proofs
1.4.1 Inductions on Integers
1.4.2 More General Forms of Integer Inductions
1.4.3 Structural Inductions
1.4.4 Mutual Inductions
1.5 The Central Concepts of Automata Theory
1.5.1 Alphabets
1.5.2 , Strings
1.5.3 Languages
1.5.4 Problems
1.6 Summary of Chapter 1
1.7 Gradiance Problems for Chapter 1
1.8 References for Chapter 1
2 Finite Automata
2.1 An Informal Picture of Finite Automata
2.1.1 The Ground Rules
2.1.2 The Protocol
2.1.3 Enabling the Automata to Ignore Actions
2.1.4 The Entire System as an Automaton
2.1.5 Using the Product Automaton to Validate the Protocol
2.2 Deterministic Finite Automata
2.2.1 Definition of a Deterministic Finite Automaton
2.2.2 How a DFA Processes Strings
2.2.3 Simpler Notations for DFA's
2.2.4 Extending the Transition Function to Strings
2.2.5 The Language of a DFA
2.2.6 Exercises for Section 2.2
2.3 Nondeterministic Finite Automata
2.3.1 An Informal View of Nondeterministic Finite Automata
2.3.2 Definition of Nondeterministic Finite Automata
2.3.3 The Extended Transition Function
2.3.4 The Language of an NFA
2.3.5 Equivalence of Deterministic and Nondeterministic Finite Automata
2.3.6 A Bad Case for the Subset Construction
2.3.7 Exercises for Section 2.3
2.4 An Application: Text Search
2.4.1 Finding Strings in Text
2.4.2 Nondeterministic Finite Automata for Text Search
2.4.3 A DFA to Recognize a Set of Keywords
2.4.4 Exercises for Section 2.4
2.5 Finite Automata With Epsilon-Transitions
2.5.1 Uses of e-Transitions
2.5.2 The Formal Notation for an c-NFA
2.5.3 Epsilon-Closures
2.5.4 Extended Transitions and Languages for c-NFA's
2.5.5 Eliminating e-Transitions
2.5.6 Exercises for Section 2.5
2.6 Summary of Chapter 2
2.7 Gradiance Problems for Chapter 2
2.8 References for Chapter 2
3 Regular Expressions and Languages
3.1 Regular Expressions
3.1.1 The Operators of Regular Expressions
3.1.2 Building Regular Expressions
3.1.3 Precedence of Regular-Expression Operators
3.1.4 Exercises for Section 3.1
3.2 Finite Automata and Regular Expressions
3.2.1 From DFA's to Regular Expressions
3.2.2 Converting DFA's to Regular Expressions by Eliminating States
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4 Properties kf Regular Languages
5 Context-Free Grammars and Languages
6 Pushdown Automata
7 Properties of Context-Free Languages
8 Introduction to Turing Machines
9 Undecidability
10 Intractable Problems
11 Additional Classes of Problems
Index
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